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A233587 Coefficients of the generalized continued fraction expansion sqrt(7) = a(1) +a(1)/(a(2) +a(2)/(a(3) +a(3)/(a(4) +a(4)/....))). 11
2, 3, 30, 34, 111, 235, 3775, 5052, 7352, 9091, 34991, 35530, 53424, 57290, 66023, 1409179, 1519111, 1725990, 1812396, 4370835, 4507156, 4655396, 44257080, 234755198, 261519946, 264374278, 273487975 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For more details on Blazys' expansions, see A233582.

Sqrt(7) is the first square root of a natural number with an a-periodic Blazys' expansion (see A233592 and A233593).

LINKS

Stanislav Sykora, Table of n, a(n) for n = 1..1000

FORMULA

sqrt(7) = 2+2/(3+3/(30+30/(34+34/(111+...)))).

MATHEMATICA

BlazysExpansion[n_, mx_] := Block[{k = 1, x = n, lmt = mx + 1, s, lst = {}}, While[k < lmt, s = Floor[x]; x = 1/(x/s - 1); AppendTo[lst, s]; k++]; lst]; BlazysExpansion[Sqrt@7, 32] (* Robert G. Wilson v, May 22 2014 *)

PROG

(PARI) bx(x, nmax)={local(c, v, k); // Blazys expansion function

v = vector(nmax); c = x; for(k=1, nmax, v[k] = floor(c); c = v[k]/(c-v[k]); ); return (v); }

bx(sqrt(7), 1000) // Execution; use very high real precision

CROSSREFS

Cf. Blazys' expansions: A233582 (Pi), A233583 (e), A233584 (sqrt(e)), A233585 (1/gamma), A233585 (2*gamma) and Blazys' continued fractions: A233588, A233589, A233590, A233591.

Cf. A010465, A010121.

Sequence in context: A278861 A024631 A032814 * A228269 A167453 A095927

Adjacent sequences:  A233584 A233585 A233586 * A233588 A233589 A233590

KEYWORD

nonn

AUTHOR

Stanislav Sykora, Jan 06 2014

STATUS

approved

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Last modified May 23 04:09 EDT 2017. Contains 286909 sequences.